Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

Abstract

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schrödinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

References in corpus (17)

• ExoMol: molecular line lists for exoplanet and other atmospheres
• ExoMol line lists IV: The rotation-vibration spectrum of methane up to 1500 K
• ExoMol molecular line lists - XVI: The rotation-vibration spectrum of hot H${}_2$S
• ExoMol line lists VII: The rotation-vibration spectrum of phosphine up to 1500 K
• The spectrum of hot methane in astronomical objects using a comprehensive computed line list
• Vibrational transition moments of CH${}_4$ from first principles
• ExoMol line lists VIII: A variationally computed line list for hot formaldehyde
• The ExoMol project: Software for computing large molecular line lists
• Accurate \textit{ab initio} vibrational energies of methyl chloride
• A Computed Room Temperature Line List for Phosphine
• A highly accurate {\it ab initio} potential energy surface for methane
• ExoMol molecular line lists - XVII The rotation-vibration spectrum of hot SO${}_3$
• A global potential energy surface and dipole moment surface for silane
• ExoMol line lists XV: A new hot line list for hydrogen peroxide
• Accurate Prediction of the Ammonia Probes of a Variable Proton-to-Electron Mass Ratio
• A global \textit{ab initio} dipole moment surface for methyl chloride
• A hybrid variational-perturbation calculation of the ro-vibrational spectrum of nitric acid

Cited by in corpus (30)

• ExoMol molecular line lists XXXV: a rotation-vibration line list for hot ammonia
• ExoMol line lists -- XXXIX. Ro-vibrational molecular line list for CO${}_2$
• ExoMol molecular line lists -- XXXVII: spectra of acetylene
• ExoMol molecular line lists - XXVII: spectra of C2H4
• ExoMol line lists -- XXXVIII. High-temperature molecular line list of silicon dioxide (SiO${}_2$)
• A Variationally Computed IR Line List for the Methyl Radical CH${}_3$
• RichMol: A general variational approach for rovibrational molecular dynamics in external electric fields
• ExoMol line lists -- XLI. High-temperature molecular line lists for the alkali metal hydroxides KOH and NaOH
• The high-temperature rotation-vibration spectrum and rotational clustering of silylene (SiH${}_2$)
• Climbing the rotational ladder to chirality
• ExoMol line lists -- XL. Ro-vibrational molecular line list for the hydronium ion (H${}_3$O${}^{+}$)
• ExoMol line lists - XXIX. The rotation-vibration spectrum of methyl chloride up to 1200 K
• The rotation-vibration spectrum of methyl fluoride from first principles
• First observation of electric-quadrupole infrared transitions in water vapour
• Electric quadrupole transitions in carbon dioxide
• ExoMol line lists -- LIX. High-temperature line list for N${}_2$O
• General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules
• Laser-induced dynamics of molecules with strong nuclear quadrupole coupling
• A variationally computed room temperature line list for AsH${}_3$
• Theoretical rotation-vibration spectroscopy of {\it cis}- and {\it trans}-diphosphene (P${}_2$H${}_2$) and the deuterated species P${}_2$HD
• Coherent Control of the Rotation Axis of Molecular Superrotors
• ExoMol line lists -- LX. Molecular line list for the ammonia isotopologue ${}^{15}$NH${}_3$
• Variational Vibrational States of Methanol (12D)
• Hyperfine-resolved rotation-vibration line list of ammonia (NH${}_3$)
• Modelling the non-local thermodynamic equilibrium spectra of silylene (SiH2)
• The nuclear-spin-forbidden rovibrational transitions of water from first principles
• Controlling rotation in the molecular-frame with an optical centrifuge
• Transferability and interpretability of vibrational normalizing-flow coordinates
• Anomalous phosphine sensitivity coefficients as probes for a possible variation of the proton-to-electron mass ratio
• Automated AFGL quantum number assignment for CO${}_2$ isotopologues using a graph neural network